Homework Help: calculus

Posted by katarina on Tuesday, May 15, 2012 at 7:40pm.

1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x+3). Show the integral used, the limits of integration and how to evaluate the integral.
2. Find the area of the region bounded by x=y^2+6, x=0 , y=-6, and y=7. Show all work required in #1.
3. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about y=3. Show the integral and give an exact answer.

calculus - Reiny, Tuesday, May 15, 2012 at 9:44pm
There are 3 questions here.
You show no work , nor do you tell us where your difficulty is.

I will start you off with #1

we need their intersection points
x^2 + 6x + 9 = 5x + 15
x^2 + x - 6 = 0
(x+3)(x-2) = 0
x = -3 or x = 2
if x = -3, y = 0
if x = 2 , y = 25

from x = -3 to x = 2, g(x) > f(x), so the effective height
= 5x + 15 - x^2 - 6x - 9
= 6 - x - x^2

Area = ∫(6 - x - x^2) dx from x = -3 to 2
= [6x - (1/2)x^2 - (1/3)x^3] from -3 to 2
= (12 - (1/2)(4) - (1/3)(8) ) - (-18 - (1/2)(9) - (1/3)(-27) )
= 12 - 2 - 8/3 + 18 - 9/2 + 9
= 179/6

Answer this Question

Related Questions

integral calculus - FIND THE AREA OF THE REGION BOUNDED BY THE CURVES Y= X^2 + ...
calculus - Use a double integral to find the area of the smaller region bounded ...
Calculus - Find the area of the region bounded by the line y=3x and y= x^3 + 2x^...
Calculus AB - Let R be the region bounded by the graphs of y=sin(pi x) and y=(x^...
calculus - A region is bounded by the function y=2x^2+3 and the x-axis over the ...
Calculus - 1. Find the are between the curves y=e^x and y=4-x^2 graphically. a...
calculus - let R be the region bounded by the graphs of y = sin(pie times x) and...
calculus - Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real ...
calculus - Write the definite integral for the area of the region bounded by the...
Calculus - *Note I reposted this question as I changed the subject** The Region...

For Further Reading

First Name:
School Subject:
Answer: